Problem: The length of a rectangular playground exceeds twice its width by 25 feet, and the perimeter of the playground is 650 feet. What is the area of the playground in square feet?
Answer: If the width of the rectangular playground is $w$, then the length is $2w + 25$. A perimeter of 650 feet means the semi-perimeter is 325 feet. The width plus the length equals the semi-perimeter, so $w + 2w + 25 = 325$. That means $3w = 300$, so $w = 100$ feet. The length must be $2 \times 100 + 25 =
225$. The area of the playground is $100 \times 225 = \boxed{22,500}$ square feet.